AI 中文总结
该研究提出保角映射方法（CMM），经克尔验证后应用于双黑洞并合，可在固定参考系中计算非轴对称黑洞的多极矩，适用于无稳定对称轴的动力学视界几何研究。
AI 中文摘要
我们提出一种数值方法，用于在黑洞视界上构建几何定义的坐标，无需假设轴对称性即可从中计算多极矩。该方法被命名为保角映射方法（CMM），是对Ashtekar等人2022年提出的保角构造的数值实现，结合了离散里奇流、到单位球的谱嵌入，以及通过零面积偶极子条件实现的莫比乌斯规范固定。我们首先针对解析克尔基准测试了CMM，随后将其应用于等质量无自旋双黑洞并合，还将其与基于近似对称性的方法进行了比较。CMM可使多极矩在固定参考系中表示，而当优选近似轴发生变化时，适配对称性的参考系会突然重新定向。在与轨道角动量对齐的参考系中，四极模的振幅在旋进阶段增长，在并合后衰减，呈现出定性的铃宕行为。这些结果表明，CMM是研究无稳定对称轴的动力学情形下视界几何的有用工具。
英文摘要
We present a numerical method that constructs geometrically defined coordinates on black-hole horizons, from which the multipole moments are computed without assuming axisymmetry. This method, which we denote the conformal-mapping method (CMM), provides a numerical realization of the conformal construction proposed by Ashtekar et al. in 2022, combining discrete Ricci flow, spectral embedding onto the unit sphere, and Möbius gauge fixing by the vanishing-area-dipole condition. We first test the CMM against analytic Kerr benchmarks, and then apply it to an equal-mass, non-spinning binary black-hole merger. We also compare it with an approximate-symmetry-based method. The CMM allows the multipole moments to be expressed in a fixed reference frame, whereas the symmetry-adapted frame can reorient abruptly when the preferred approximate axis changes. In a frame aligned with the orbital angular momentum, the amplitude of the quadrupole mode grows during inspiral and decays after merger, displaying a qualitative ringdown behavior. These results show that the CMM is a useful tool for studying horizon geometry in dynamical situations where no stable symmetry axis is available.
Comments14 pages, 6 figures
